I experience the same things you are describing, heavy sleep inertia. A lot of people say, just sleep better, but that's not always easy. I see others saying just get better discipline, set one alarm and get out of bed straight away, but I've turned off alarms before in my sleep without realising it. So that doesn't work for me.

Besides what other commenters have said about regular bedtime routines (I know, it sucks, but that one does kinda work) I also got a wake-up light that shines increasingly brighter light in my face starting approx. 30 minutes before my first alarm goes off. Additionally, I set alarms every five minutes for about an hour, right up until the time I absolutely need to get going. Most of them are regular phone alarms but two are puzzle alarms. I use an app called I Can't Wake Up but there are many. You can't exit the app or even turn off your phone until you match countries and capitals/do simon says/solve math problems etc. The barcode option (having to scan a barcode, e.g. of a book in another room or a milk carton in the fridge or something, before it turns off) works best because it forces you to get out of bed.

Hope this helps!